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Abstract : The book is part of a trilogy covering the field of Markov processes and provides a readable and constructive treatment of Brownian motion and diffusion. It contains some of the author's own research and many of the proofs are new. It dispenses with most of the customary transform apparatus, and the chapter on Brownian motion emphasizes topics which haven't had much textbook coverage, such as square variation, the reflection principle, and the invariance principle. The chapter on diffusion shows how to obtain the process from Brownian by changing time. (Author)
Serfling et al. (Wed,) studied this question.